What kind cup and bowl is this? Thank you for your answers!

It seems an earthenware ceramics as it is glazed all throughout including the bottom.Does not seem transparent hence not
Porcelain.
TTA

 

Porcelain can be glazed all throughout as any other type of pottery. If a porcelain piece is with thick walls you won't be able to see through. Plus, it's hard to tell from the pictures, you have to hold it against the light.
I am not saying that it is not earthenware, could be.
I think the OP is asking more like what are they used for rather than made of.

 

Kardi ..as to glazing I was just comparing earthenware with stoneware which is not glazed at the bottom.I guess porcelains are glazed always if I am not mistaken..yes we need to put against a light...but from their look they rather seem opaque..
TTA
TTA

 

Porcelain can be left unglazed, the whole piece, whatever it is. I guess such is called bisque porcelain.
What do you mean that stoneware is not glazed on the bottom? You mean the base or the foot ring? Or both? Usually the foot rim is unglazed, the base can be glazed or not. Can't tell from the pics if the OP pieces have glaze or not on the feet.

 

You may be right on the porcelain...but the base of stonewares are left unglazed usually..it also depends on the intended use..bottom unglazed stonewares can hold liquid...but bottom unglazed earthenware can not...hence earthenware intended to hold liquid have to be bottom glazed but that is not necessary for stoneware.

TTA

 

Please give sizes. Impossible to guess use without the size.
Don